Where there is a visible frost on the surface the grass plant becomes brittle as it is 90% water & can be easily crushed. As a consequence play in these conditions will cause the plant to die. (Similar to cracking an egg shell. Once its broken it can’t be put back together.)
Similarly even where there is not a visible frost & the top 2 inches of top-soil have thawed, the sub-soil may still be frozen. Play on the greens in such circumstances will cause root break where the underlying roots are severed causing the plant to die.
Damage may not be immediately evident but within 2 / 3 days the leaves will turn brown & the plant will die. This causes thinning of the grass coverage & weakens the remaining plants. This in turn makes the surface more susceptible to disease & weed ingress. At the start of the new season the greens will take longer to recover & the quality of the putting surfaces will be compromised until mid season.